Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 439

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\[1)\ x^{4} = 256;\]

\[x^{4} - 256 = 0;\]

\[\left( x^{2} - 16 \right)\left( x^{2} + 16 \right) = 0;\]

\[\left( x^{2} - 16 \right) = 0;\]

\[(x - 4)(x + 4) = 0;\]

\[x_{1} = 4\ \ и\ \ x_{2} = - 4;\]

\[Ответ:\ \ x = \pm 4.\]

\[2)\ x^{5} = - \frac{1}{32};\]

\[x = \sqrt[5]{- \frac{1}{32}} = - \sqrt[5]{\left( \frac{1}{2} \right)^{5}} = - \frac{1}{2}.\]

\[Ответ:\ \ x = - 0,5.\]

\[3)\ 5x^{5} = - 160;\]

\[x^{5} = - 32;\]

\[x = \sqrt[5]{- 32} = - \sqrt[5]{2^{5}} = - 2.\]

\[Ответ:\ \ x = - 2.\]

\[4)\ 2x^{6} = 128;\]

\[x^{6} = 64;\]

\[x = \pm \sqrt[6]{64} = \pm \sqrt[6]{2^{6}} = \pm 2.\]

\[Ответ:\ \ x = \pm 2.\]